How good are projection methods for convex feasibility problems?

We consider simple projection methods for solving convex feasibility problems. Both successive and sequential methods are considered, and heuristics to improve these are suggested. Unfortunately, particularly given the large literature which might make one think otherwise, numerical tests indicate that in general none of the variants considered are especially effective or competitive with more sophisticated alternatives

Finding a point in the relative interior of a polyhedron

A new initialization or `Phase I' strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points - an all-pervasive assumption in interior point method theory that implies the existence of the central path - our initial method (Algorithm 1) is globally Q-linearly and asymptotically Q-quadratically convergent, with a provable worst-case iteration complexity bound. When this assumption is not met, the numerical behaviour of Algorithm 1 is highly disappointing, even when the problem is primal-dual feasible. This is due to the presence of implicit equalities, inequality constraints that hold as equalities at all the feasible points. Controlled perturbations of the inequality constraints of the primal-dual problems are introduced - geometrically equivalent to enlarging the primal-dual feasible region and then systematically contracting it back to its initial shape - in order for the perturbed problems to satisfy the assumption. Thus Algorithm 1 can successfully be employed to solve each of the perturbed problems.\ud We show that, when there exist primal-dual strictly feasible points of the original problems, the resulting method, Algorithm 2, finds such a point in a finite number of changes to the perturbation parameters. When implicit equalities are present, but the original problem and its dual are feasible, Algorithm 2 asymptotically detects all the primal-dual implicit equalities and generates a point in the relative interior of the primal-dual feasible set. Algorithm 2 can also asymptotically detect primal-dual infeasibility. Successful numerical experience with Algorithm 2 on linear programs from NETLIB and CUTEr, both with and without any significant preprocessing of the problems, indicates that Algorithm 2 may be used as an algorithmic preprocessor for removing implicit equalities, with theoretical guarantees of convergence

Nonlinear programming without a penalty function or a filter

A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate that the method performs well

Remembering Wassily Hoeffding

Wasssily Hoeffding's terminal illness and untimely death in 1991 put an end to efforts that were made to interview him for Statistical Science. An account of his scientific work is given in Fisher and Sen [The Collected Works of Wassily Hoeffding (1994) Springer], but the present authors felt that the statistical community should also be told about the life of this remarkable man. He contributed much to statistical science, but will also live on in the memory of those who knew him as a kind and modest teacher and friend, whose courage and learning were matched by a wonderful sense of humor.Comment: Published in at http://dx.doi.org/10.1214/08-STS271 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A gap analysis of confined field trial application forms for genetically modified crops in East Africa: evaluating the potential for harmonization

"The regulatory approval of genetically modified crops in the field initially requires small, restricted experimental trials known as confined field trials. These small scale experiments provide researchers with important information on environmental interactions and agronomic performance of the crop in a safe and contained manner. To authorize confined field trials regulatory review is required, with formats for obtaining relevant information differing from country to country. In this paper, a Gap Analysis is used to identify informational gaps and potential for harmonization of confined field trial application processes in three East African countries - Tanzania, Kenya, and Uganda. The basic principle behind gap analysis is a comparison of the status quo to an ideal with the identification of the differences or gaps and the difficulty involved in removing the gaps. The resulting similarity of the application forms provides a potential basis for harmonization of confined field trial application processes between countries leading to potential efficiency gains." Authors' abstractGenetically modified crops, Gap analysis, Confined field trials, biotechnology,

The Foaming Three-Charge Black Hole

We find a very large set of smooth horizonless geometries that have the same charges and angular momenta as the five-dimensional, maximally-spinning, three-charge, BPS black hole (J^2 = Q^3). Our solutions are constructed using a four-dimensional Gibbons-Hawking base space that has a very large number of two-cycles. The entropy of our solutions is proportional to Q^(1/2). In the same class of solutions we also find microstates corresponding to zero-entropy black rings, and these are related to the microstates of the black hole by continuous deformations.Comment: 14 pages, harvma

Strategies for the control of Rhipicephalus microplus ticks in a world of conventional acaricide and macrocyclic lactone resistance

Infestations with the cattle tick, Rhipicephalus microplus, constitute the most important ectoparasite problem for cattle production in tropical and subtropical regions worldwide, resulting in major economic losses. The control of R. microplus is mostly based on the use of conventional acaricides and macrocyclic lactones. However, the intensive use of such compounds has resulted in tick populations that exhibit resistance to all major acaricide chemical classes. Consequently, there is a need for the development of alternative approaches, possibly including the use of animal husbandry practices, synergized pesticides, rotation of acaricides, pesticide mixture formulations, manual removal of ticks, selection for host resistance, nutritional management, release of sterile male hybrids, environmental management, plant species that are unfavourable to ticks, pasture management, plant extracts, essential oils and vaccination. Integrated tick management consists of the systematic combination of at least two control technologies aiming to reduce selection pressure in favour of acaricide-resistant individuals, while maintaining adequate levels of animal production. The purpose of this paper is to present a current review on conventional acaricide and macrocyclic lactone resistance for better understanding and control of resistant ticks with particular emphasis on R. microplus on cattle